Question
According to a recent report, 67% of Internet searches in a particular month used the Google search engine. Assume that a sample of 25 searches is studied. What's the probability that exactly 20 of them used Google? Round answer to four decimal places
Answers
GPT 3.5
To find the probability of exactly 20 searches using Google out of 25, we can use the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where:
n = 25 (total number of searches)
k = 20 (number of searches using Google)
p = 0.67 (probability of using Google)
Plugging in the values:
P(X = 20) = (25 choose 20) * (0.67)^20 * (0.33)^5
Calculating the values:
P(X = 20) = (25! / (20! * 5!)) * (0.67)^20 * (0.33)^5
P(X = 20) = 53,130 * 0.00000447 * 0.002275
P(X = 20) = 0.2455
Therefore, the probability that exactly 20 out of 25 searches use Google is 0.2455 (rounded to four decimal places).
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where:
n = 25 (total number of searches)
k = 20 (number of searches using Google)
p = 0.67 (probability of using Google)
Plugging in the values:
P(X = 20) = (25 choose 20) * (0.67)^20 * (0.33)^5
Calculating the values:
P(X = 20) = (25! / (20! * 5!)) * (0.67)^20 * (0.33)^5
P(X = 20) = 53,130 * 0.00000447 * 0.002275
P(X = 20) = 0.2455
Therefore, the probability that exactly 20 out of 25 searches use Google is 0.2455 (rounded to four decimal places).